Thank you for visiting Divide the following polynomials 35 tex frac 9x 6 3 tex 36 tex frac 4x 7 2 tex 37 tex frac x 2 3x 5. This page is designed to guide you through key points and clear explanations related to the topic at hand. We aim to make your learning experience smooth, insightful, and informative. Dive in and discover the answers you're looking for!
Answer :
Sure, let's go through the polynomial division step-by-step for each question:
35. Divide [tex]\( \frac{9x - 6}{3} \)[/tex]:
- Divide each term by 3:
[tex]\[ \frac{9x}{3} = 3x \][/tex]
[tex]\[ \frac{-6}{3} = -2 \][/tex]
- So, the result is [tex]\( 3x - 2 \)[/tex].
36. Divide [tex]\( \frac{4x - 7}{2} \)[/tex]:
- Divide each term by 2:
[tex]\[ \frac{4x}{2} = 2x \][/tex]
[tex]\[ \frac{-7}{2} = -\frac{7}{2} \][/tex]
- The result is [tex]\( 2x - \frac{7}{2} \)[/tex].
37. Divide [tex]\( \frac{x^2 - 3x + 5}{x} \)[/tex]:
- Divide each term by [tex]\( x \)[/tex]:
[tex]\[ \frac{x^2}{x} = x \][/tex]
[tex]\[ \frac{-3x}{x} = -3 \][/tex]
[tex]\[ \frac{5}{x} \text{ can't be simplified and remains } 5 .\][/tex]
- The result is [tex]\( x - 3 + \frac{5}{x} \)[/tex].
38. Divide [tex]\( \frac{5x^2 - 25x + 2}{-5x} \)[/tex]:
- Divide each term by [tex]\( -5x \)[/tex]:
[tex]\[ \frac{5x^2}{-5x} = -x \][/tex]
[tex]\[ \frac{-25x}{-5x} = 5 \][/tex]
[tex]\[ \frac{2}{-5x} \text{ gives a remainder }.\][/tex]
- The result is [tex]\( -x + 5 + \frac{2}{-5x} \)[/tex].
39. Divide [tex]\( \frac{4x^{10} - 5x^9 - 20x^4}{4x^2} \)[/tex]:
- Divide each term by [tex]\( 4x^2 \)[/tex]:
[tex]\[ \frac{4x^{10}}{4x^2} = x^8 \][/tex]
[tex]\[ \frac{-5x^9}{4x^2} = -\frac{5}{4}x^7 \][/tex]
[tex]\[ \frac{-20x^4}{4x^2} = -5x^2 \][/tex]
- The result is [tex]\( x^8 - \frac{5}{4}x^7 - 5x^2 \)[/tex].
40. Divide [tex]\( \left(-x^6 + x^5 + 7x^2 - 9\right) \div x^4 \)[/tex]:
- Divide each term by [tex]\( x^4 \)[/tex]:
[tex]\[ \frac{-x^6}{x^4} = -x^2 \][/tex]
[tex]\[ \frac{x^5}{x^4} = x \][/tex]
[tex]\[ \frac{7x^2}{x^4} = \frac{7}{x^2} \text{ which remains in the solution} \][/tex]
[tex]\[ \frac{-9}{x^4} = -\frac{9}{x^4} \][/tex]
- The result is [tex]\( -x^2 + x + \frac{7x^2 - 9}{x^4} \)[/tex].
41. Divide [tex]\( \left(x^2 + 2x + 6\right) \div x \)[/tex]:
- Divide each term by [tex]\( x \)[/tex]:
[tex]\[ \frac{x^2}{x} = x \][/tex]
[tex]\[ \frac{2x}{x} = 2 \][/tex]
[tex]\[ \frac{6}{x} \text{ remains } 6 \][/tex]
- The result is [tex]\( x + 2 + \frac{6}{x} \)[/tex].
42. Divide [tex]\( \left(3x^2 - 15x + 5\right) \div (-3x) \)[/tex]:
- Divide each term by [tex]\( -3x \)[/tex]:
[tex]\[ \frac{3x^2}{-3x} = -x \][/tex]
[tex]\[ \frac{-15x}{-3x} = 5 \][/tex]
[tex]\[ \frac{5}{-3x} \text{ remains as a remainder} \][/tex]
- The result is [tex]\( -x + 5 + \frac{5}{-3x} \)[/tex].
43. Divide [tex]\( \left(2x^{11} - 5x^7 - 10x^6\right) \div 2x^3 \)[/tex]:
- Divide each term by [tex]\( 2x^3 \)[/tex]:
[tex]\[ \frac{2x^{11}}{2x^3} = x^8 \][/tex]
[tex]\[ \frac{-5x^7}{2x^3} = -\frac{5}{2}x^4 \][/tex]
[tex]\[ \frac{-10x^6}{2x^3} = -5x^3 \][/tex]
- The result is [tex]\( x^8 - \frac{5}{2}x^4 - 5x^3 \)[/tex].
44. Divide [tex]\( \left(-2x^6 + 5x^5 + 9x^2 + 2\right) \div x^4 \)[/tex]:
- Divide each term by [tex]\( x^4 \)[/tex]:
[tex]\[ \frac{-2x^6}{x^4} = -2x^2 \][/tex]
[tex]\[ \frac{5x^5}{x^4} = 5x \][/tex]
[tex]\[ \frac{9x^2}{x^4} = \frac{9}{x^2} \][/tex]
[tex]\[ \frac{2}{x^4} = \frac{2}{x^4} \][/tex]
- The result is [tex]\( -2x^2 + 5x + \frac{9x^2 + 2}{x^4} \)[/tex].
These steps help understand how each polynomial division is carried out. If you need further clarification on any specific step, feel free to ask!
35. Divide [tex]\( \frac{9x - 6}{3} \)[/tex]:
- Divide each term by 3:
[tex]\[ \frac{9x}{3} = 3x \][/tex]
[tex]\[ \frac{-6}{3} = -2 \][/tex]
- So, the result is [tex]\( 3x - 2 \)[/tex].
36. Divide [tex]\( \frac{4x - 7}{2} \)[/tex]:
- Divide each term by 2:
[tex]\[ \frac{4x}{2} = 2x \][/tex]
[tex]\[ \frac{-7}{2} = -\frac{7}{2} \][/tex]
- The result is [tex]\( 2x - \frac{7}{2} \)[/tex].
37. Divide [tex]\( \frac{x^2 - 3x + 5}{x} \)[/tex]:
- Divide each term by [tex]\( x \)[/tex]:
[tex]\[ \frac{x^2}{x} = x \][/tex]
[tex]\[ \frac{-3x}{x} = -3 \][/tex]
[tex]\[ \frac{5}{x} \text{ can't be simplified and remains } 5 .\][/tex]
- The result is [tex]\( x - 3 + \frac{5}{x} \)[/tex].
38. Divide [tex]\( \frac{5x^2 - 25x + 2}{-5x} \)[/tex]:
- Divide each term by [tex]\( -5x \)[/tex]:
[tex]\[ \frac{5x^2}{-5x} = -x \][/tex]
[tex]\[ \frac{-25x}{-5x} = 5 \][/tex]
[tex]\[ \frac{2}{-5x} \text{ gives a remainder }.\][/tex]
- The result is [tex]\( -x + 5 + \frac{2}{-5x} \)[/tex].
39. Divide [tex]\( \frac{4x^{10} - 5x^9 - 20x^4}{4x^2} \)[/tex]:
- Divide each term by [tex]\( 4x^2 \)[/tex]:
[tex]\[ \frac{4x^{10}}{4x^2} = x^8 \][/tex]
[tex]\[ \frac{-5x^9}{4x^2} = -\frac{5}{4}x^7 \][/tex]
[tex]\[ \frac{-20x^4}{4x^2} = -5x^2 \][/tex]
- The result is [tex]\( x^8 - \frac{5}{4}x^7 - 5x^2 \)[/tex].
40. Divide [tex]\( \left(-x^6 + x^5 + 7x^2 - 9\right) \div x^4 \)[/tex]:
- Divide each term by [tex]\( x^4 \)[/tex]:
[tex]\[ \frac{-x^6}{x^4} = -x^2 \][/tex]
[tex]\[ \frac{x^5}{x^4} = x \][/tex]
[tex]\[ \frac{7x^2}{x^4} = \frac{7}{x^2} \text{ which remains in the solution} \][/tex]
[tex]\[ \frac{-9}{x^4} = -\frac{9}{x^4} \][/tex]
- The result is [tex]\( -x^2 + x + \frac{7x^2 - 9}{x^4} \)[/tex].
41. Divide [tex]\( \left(x^2 + 2x + 6\right) \div x \)[/tex]:
- Divide each term by [tex]\( x \)[/tex]:
[tex]\[ \frac{x^2}{x} = x \][/tex]
[tex]\[ \frac{2x}{x} = 2 \][/tex]
[tex]\[ \frac{6}{x} \text{ remains } 6 \][/tex]
- The result is [tex]\( x + 2 + \frac{6}{x} \)[/tex].
42. Divide [tex]\( \left(3x^2 - 15x + 5\right) \div (-3x) \)[/tex]:
- Divide each term by [tex]\( -3x \)[/tex]:
[tex]\[ \frac{3x^2}{-3x} = -x \][/tex]
[tex]\[ \frac{-15x}{-3x} = 5 \][/tex]
[tex]\[ \frac{5}{-3x} \text{ remains as a remainder} \][/tex]
- The result is [tex]\( -x + 5 + \frac{5}{-3x} \)[/tex].
43. Divide [tex]\( \left(2x^{11} - 5x^7 - 10x^6\right) \div 2x^3 \)[/tex]:
- Divide each term by [tex]\( 2x^3 \)[/tex]:
[tex]\[ \frac{2x^{11}}{2x^3} = x^8 \][/tex]
[tex]\[ \frac{-5x^7}{2x^3} = -\frac{5}{2}x^4 \][/tex]
[tex]\[ \frac{-10x^6}{2x^3} = -5x^3 \][/tex]
- The result is [tex]\( x^8 - \frac{5}{2}x^4 - 5x^3 \)[/tex].
44. Divide [tex]\( \left(-2x^6 + 5x^5 + 9x^2 + 2\right) \div x^4 \)[/tex]:
- Divide each term by [tex]\( x^4 \)[/tex]:
[tex]\[ \frac{-2x^6}{x^4} = -2x^2 \][/tex]
[tex]\[ \frac{5x^5}{x^4} = 5x \][/tex]
[tex]\[ \frac{9x^2}{x^4} = \frac{9}{x^2} \][/tex]
[tex]\[ \frac{2}{x^4} = \frac{2}{x^4} \][/tex]
- The result is [tex]\( -2x^2 + 5x + \frac{9x^2 + 2}{x^4} \)[/tex].
These steps help understand how each polynomial division is carried out. If you need further clarification on any specific step, feel free to ask!
Thank you for reading the article Divide the following polynomials 35 tex frac 9x 6 3 tex 36 tex frac 4x 7 2 tex 37 tex frac x 2 3x 5. We hope the information provided is useful and helps you understand this topic better. Feel free to explore more helpful content on our website!
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